Question: Find all solutions to the equation $\sqrt{5+2z} = 11$.
Explanation: We square both sides to get rid of the square root sign.  This gives us $5+2z = 121$.  Solving for $z$ gives $z = \boxed{58}$.  We squared an equation, so we have to test our solution to make sure it isn't extraneous.  We have
\[\sqrt{5 +2 \cdot 58} =\sqrt{121} = 11\]so our solution is valid.